Optimized aerodynamic profile for a turbine blade, in particular for a rotary wheel of the fourth stage of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Z′ given in Table 1, in which the coordinate Z′ is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

The present invention relates to an aerodynamic profile for a turbineblade.

In particular, the invention relates to the aerodynamic profile of ablade of a rotary wheel of a gas turbine, and more particularly of a lowpressure turbine of the type used in a turbojet of an aircraft.

The invention relates in particular to a blade of the rotary wheel ofthe fourth stage of a turbine having a plurality of stages, preferablyfour stages.

Such a profile should enable the turbine to provide the desiredefficiency, and in order to do that it must be such that the flow of airaround the profile is sound, i.e. substantially such that it does notgive rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of theengine, and in particular, for the blade of a rotary wheel forming aportion of the rotor of the turbine, it must be capable of beingfastened easily to the support disk of the rotary wheel, via the root ofthe blade, whereas its tip must be capable of carrying a top platform.Furthermore, this part must be capable of being obtained by casting, andmust therefore present a profile that is compatible with thatmanufacturing technique.

Furthermore, the profile of the blade must enable it to withstand themechanical stresses to which the blade is subjected, by enabling thosestresses to be spread over the entire blade in such a manner as to avoidpremature wear thereof. This spreading must apply both in static modeand in dynamic mode. In particular, it must be such that the blade,given its resonant modes, can withstand the highest dynamic loading forgood operation of the turbine.

An object of the invention is to propose an aerodynamic profile for aturbine blade that is optimized, and capable of satisfying thoseobjectives.

This object is achieved by the fact that when cold and in a non-coatedstate, said profile is substantially identical to a nominal profiledetermined by the Cartesian coordinates X,Y,Z′ given in Table 1, inwhich the coordinate Z′ is the quotient D/H where D is the distance ofthe point under consideration from a reference X,Y plane situated at thebase of the nominal profile, and H is the height of said profilemeasured from said reference plane that is the intersection of thestacking axis of the set of blades and the axisymmetric surface of thehub, out to a second reference plane that is the intersection of saidstacking axis with the axisymmetric surface of the casing, themeasurements D and H being taken radially relative to the axis of theturbine, while the coordinate X is measured in the axial direction ofthe turbine.

This profile has been determined as a result of numerous tests andsimulations. It is defined cold, i.e. at an ambient temperature of 20°C. That is a reference temperature at which the profile is geometricallydetermined. The above-mentioned objectives of aerodynamics andmechanical optimization are naturally valid for the conditions of use ofthis aerodynamic profile, i.e. when hot, at a temperature that isstabilized when the engine of which the turbine forms a part is beingused under cruising conditions.

Furthermore, the aerodynamic profile of the invention is defined in thenon-coated state. Since turbine blades are subjected to high temperaturegradients, it is common practice for them to be provided with a coatinghaving thermal properties enabling them more easily to withstand suchtemperature variations. The profile is determined prior to installingsuch a coating.

It is stated above that the profile of the invention is “substantiallyidentical” to the nominal profile. This means that the profile maydepart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of±1 millimeter (mm) in a direction normal to the surface of the nominalprofile.

This variation takes account in particular of manufacturing tolerancesof the profile.

It is also preferable for the X,Y coordinates of the aerodynamic profileto lie within a range of ±5% relative to the X,Y coordinates of thenominal profile.

This variation takes account of the setting of the profile to adapt tothe flow coming from the turbine vanes situated upstream, so as tofurther improve the efficiency of the turbine. In particular, theprofile is adapted so as to be optimized for the flow coming from thenozzle of the fourth stage of a turbine, when the blade of the inventionbelongs to the rotary wheel of the fourth stage of a turbine.

For a blade of a rotary wheel, forming a portion of the rotor of aturbine, the profile serves to optimize the inter-blade flow, i.e. theflow between adjacent blades of the wheel, and thus transforms a maximumamount of the kinetic energy of the gaseous fluid into kinetic energy onthe shaft of the turbine. In addition, it serves to orient the gaseousfluid correctly for the turbine vanes situated downstream, in particularbelonging to the stationary nozzle of the next stage of the turbine, ifsuch a next stage exists.

The invention can be better understood and its advantages appear betteron reading the following detailed description of an embodiment given byway of non-limiting example. The description refers to the accompanyingdrawings, in which:

FIG. 1 is a fragmentary axial section view of a turbine including ablade of profile that corresponds to that of the invention;

FIG. 2 is a perspective view of a blade to which the invention applies;and

FIG. 3 is a diagrammatic section view of the FIG. 2 blade on an X-Yplane.

The turbine shown in axial section in FIG. 1 comprises four stagesreferenced respectively E1 to E4. In the direction S going from upstreamto downstream, each stage comprises a nozzle that forms a portion of thestator of the turbine and that has a plurality of radially-orientedvanes, and a rotary wheel that forms a portion of the rotor of theturbine and that likewise includes a plurality of radially-orientedblades.

In FIG. 1, the vanes of the nozzles of stages E1 to E4 are givenreferences D1 to D4, whereas the blades of rotary wheels of stages E1 toE4 are given respective references R1 to R4.

In known manner, the vanes of the nozzles are fastened at both ends tostationary structure portions, while the blades of the rotary wheels arefastened to a rotary disk via their roots that are formed at theirradially-inner ends closer to the axis of the rotation A of the turbine.The various disks designated by respective references d1 to d4 areconstrained to rotate together. In the example shown, the tips of theblades of the rotary wheels, formed at their radially-outer ends, carrytop platforms given respective references t1 to t4.

The invention relates in particular to the blade R4 which is a blade ofthe rotary wheel of the fourth stage E4 of the turbine.

The blade R4 shown in FIG. 2 includes, at its radially-inner end, ablade root 10 enabling it to be connected to a support disk forming thehub of a turbine wheel, and a platform 12 from which an aerodynamicprofile 14 extends. At its tip, formed at its radially-outer end remotefrom the platform 12, the blade includes a top platform 16 that forms anouter casing carried by the various blades of the wheel.

By convention, the aerodynamic profile 14 is the entire portion of saidblade that extends radially from the platform 12 to the top platform 16.

In FIG. 2, there can be seen a frame of reference comprising Cartesiancoordinates X,Y,Z. The radial direction Z is the height direction of theblade, which extends radially from its root to its tip. This direction Zis perpendicular to the axial direction X which is the direction of theaxis of rotation A of the turbine. The direction Y is perpendicular tothe X,Z plane and is therefore tangential to the direction of rotationof the turbine.

The nominal profile from which the aerodynamic profile of the inventionis determined is defined in following Table 1 of coordinates, in whichthe coordinates Z′, measured along the axis Z is non-dimensional,whereas the dimensions X and Y, respectively measured along the axes Xand Y, are expressed in millimeters.

TABLE 1 X Y Z′ X Y Z′ X Y Z′ −13.6041 −2.47318 −0.15 11.45446 −3.284490.1 9.05624 −2.31757 0.6 −13.63818 −2.41269 −0.15 12.13855 −3.97778 0.18.39734 −1.67534 0.6 −13.68058 −2.32113 −0.15 12.77222 −4.63644 0.17.69343 −1.02442 0.6 −13.72688 −2.17242 −0.15 13.35569 −5.25485 0.16.94241 −0.37566 0.6 −13.7481 −1.95648 −0.15 13.88895 −5.82854 0.16.14283 0.25913 0.6 −13.70351 −1.67658 −0.15 14.37193 −6.35412 0.15.29453 0.86762 0.6 −13.56504 −1.35103 −0.15 14.80483 −6.82903 0.14.3992 1.43761 0.6 −13.32761 −0.99612 −0.15 15.18808 −7.25161 0.13.46076 1.9578 0.6 −12.99678 −0.6185 −0.15 15.52195 −7.62146 0.1 2.485332.41834 0.6 −12.57928 −0.21894 −0.15 15.80749 −7.93883 0.1 1.481252.81185 0.6 −12.08175 0.20486 −0.15 16.04639 −8.20457 0.1 0.458723.13462 0.6 −11.50779 0.65301 −0.15 16.24112 −8.42036 0.1 −0.571083.38657 0.6 −10.85388 1.11557 −0.15 16.39131 −8.59172 0.1 −1.597053.57027 0.6 −10.1123 1.5726 −0.15 16.46956 −8.74282 0.1 −2.60874 3.689860.6 −9.28131 2.00751 −0.15 16.47223 −8.86159 0.1 −3.59661 3.75019 0.6−8.36291 2.40499 −0.15 16.44267 −8.93047 0.1 −4.55206 3.75651 0.6−7.36204 2.7509 −0.15 16.40649 −8.97528 0.1 −5.46739 3.71445 0.6−6.28647 3.03353 −0.15 16.36553 −9.00845 0.1 −6.33566 3.62845 0.6−5.14618 3.24452 −0.15 16.30365 −9.03806 0.1 −7.15059 3.50303 0.6−3.9525 3.37874 −0.15 16.19517 −9.04503 0.1 −7.9068 3.34386 0.6 −2.717293.43353 −0.15 16.05177 −8.98413 0.1 −8.59978 3.15697 0.6 −1.452543.40804 −0.15 15.89125 −8.85109 0.1 −9.226 2.9487 0.6 −0.17043 3.29918−0.15 15.69497 −8.67155 0.1 −9.78341 2.72671 0.6 1.11176 3.07649 −0.1515.45166 −8.45303 0.1 −10.2722 2.50075 0.6 2.37469 2.73268 −0.1515.16331 −8.18939 0.1 −10.69604 2.28379 0.6 3.60234 2.27792 −0.1514.82866 −7.87965 0.1 −11.06132 2.08964 0.6 4.7826 1.72759 −0.1514.44747 −7.52288 0.1 −11.37349 1.92734 0.6 5.90763 1.10014 −0.1514.01958 −7.11942 0.1 −11.63452 1.79761 0.6 6.97341 0.41492 −0.1513.54538 −6.67011 0.1 −11.8525 1.71403 0.6 7.97885 −0.30924 −0.1513.02484 −6.1773 0.1 −12.02963 1.68942 0.6 8.92469 −1.05504 −0.1512.45786 −5.64441 0.1 −12.15517 1.71568 0.6 9.8124 −1.80733 −0.1511.84332 −5.07694 0.1 −12.22463 1.76141 0.6 10.64348 −2.55324 −0.1511.18012 −4.48136 0.1 −12.26099 1.80558 0.6 11.4193 −3.28188 −0.1510.46662 −3.86594 0.1 −12.13231 2.68681 0.7 12.14089 −3.98409 −0.159.70149 −3.23987 0.1 −12.15487 2.74146 0.7 12.80897 −4.65225 −0.158.88365 −2.61355 0.1 −12.16415 2.82687 0.7 13.42401 −5.28013 −0.158.01244 −1.99869 0.1 −12.13378 2.95601 0.7 13.98622 −5.86283 −0.157.08823 −1.40784 0.1 −12.03852 3.1143 0.7 14.49572 −6.3966 −0.15 6.11265−0.85424 0.1 −11.87397 3.2908 0.7 14.95258 −6.87888 −0.15 5.08888−0.35184 0.1 −11.64483 3.48636 0.7 15.35711 −7.30802 −0.15 4.022550.08638 0.1 −11.35226 3.70229 0.7 15.70989 −7.68333 −0.15 2.922170.45029 0.1 −10.99327 3.93445 0.7 16.01119 −8.00581 −0.15 1.797920.73093 0.1 −10.56653 4.1795 0.7 16.26373 −8.27542 −0.15 0.66194 0.922990.1 −10.07309 4.43686 0.7 16.46863 −8.4952 −0.15 −0.4725 1.026 0.1−9.51305 4.70305 0.7 16.6285 −8.66821 −0.15 −1.59222 1.0457 0.1 −8.885274.96967 0.7 16.71595 −8.82081 −0.15 −2.68545 0.99113 0.1 −8.188925.22528 0.7 16.7234 −8.94341 −0.15 −3.7423 0.8732 0.1 −7.4249 5.457940.7 16.69494 −9.01548 −0.15 −4.75479 0.70353 0.1 −6.59607 5.65592 0.716.65855 −9.06259 −0.15 −5.71667 0.49361 0.1 −5.70703 5.80676 0.716.61765 −9.09686 −0.15 −6.62321 0.25474 0.1 −4.76444 5.89773 0.716.55536 −9.1276 −0.15 −7.47097 −0.00251 0.1 −3.77716 5.9172 0.716.44562 −9.13586 −0.15 −8.25748 −0.26865 0.1 −2.75618 5.85505 0.716.29977 −9.0758 −0.15 −8.98111 −0.53525 0.1 −1.7143 5.70342 0.716.13546 −8.94329 −0.15 −9.64104 −0.79466 0.1 −0.66545 5.45795 0.715.93317 −8.76549 −0.15 −10.23763 −1.03895 0.1 0.3765 5.11904 0.715.68303 −8.54856 −0.15 −10.77378 −1.25646 0.1 1.39919 4.69224 0.715.38633 −8.28693 −0.15 −11.24977 −1.44397 0.1 2.39295 4.18758 0.715.04134 −7.98015 −0.15 −11.66681 −1.59769 0.1 3.35147 3.61833 0.714.64756 −7.62751 −0.15 −12.02554 −1.71696 0.1 4.27072 2.99813 0.714.2047 −7.2295 −0.15 −12.32793 −1.79848 0.1 5.14841 2.34019 0.7 13.7126−6.78761 −0.15 −12.57503 −1.84194 0.1 5.98437 1.65807 0.7 13.17117−6.30434 −0.15 −12.76706 −1.84712 0.1 6.77915 0.9641 0.7 12.57932−5.78441 −0.15 −12.90152 −1.81673 0.1 7.53291 0.2685 0.7 11.9294−5.24144 −0.15 −12.97742 −1.76962 0.1 8.24546 −0.42 0.7 11.21862−4.68535 −0.15 −13.01731 −1.72285 0.1 8.91686 −1.09342 0.7 10.44638−4.12525 −0.15 −12.89472 −1.43005 0.15 9.547 −1.74483 0.7 9.61327−3.57046 −0.15 −12.92286 −1.3696 0.15 10.13499 −2.36883 0.7 8.72127−3.03004 −0.15 −12.93524 −1.27352 0.15 10.68003 −2.96067 0.7 7.77385−2.5124 −0.15 −12.90887 −1.12626 0.15 11.18155 −3.51623 0.7 6.77589−2.02507 −0.15 −12.82303 −0.93641 0.15 11.63902 −4.03208 0.7 5.73338−1.57462 −0.15 −12.67136 −0.71045 0.15 12.0521 −4.50557 0.7 4.6532−1.16681 −0.15 −12.45525 −0.44832 0.15 12.42069 −4.93469 0.7 3.54286−0.80691 −0.15 −12.16853 −0.15515 0.15 12.74514 −5.318 0.7 2.40968−0.50224 −0.15 −11.81253 0.17 0.15 13.02627 −5.65466 0.7 1.25768−0.28039 −0.15 −11.38538 0.52426 0.15 13.26542 −5.94456 0.7 0.09743−0.1604 −0.15 −10.88393 0.90169 0.15 13.4639 −6.1886 0.7 −1.05581−0.14881 −0.15 −10.30735 1.29739 0.15 13.62719 −6.38559 0.7 −2.18639−0.23453 −0.15 −9.65557 1.70582 0.15 13.74722 −6.54621 0.7 −3.28192−0.40174 −0.15 −8.92802 2.11868 0.15 13.7969 −6.68762 0.7 −4.33362−0.63216 −0.15 −8.12393 2.52447 0.15 13.78314 −6.79125 0.7 −5.33587−0.90754 −0.15 −7.24379 2.91032 0.15 13.75167 −6.84927 0.7 −6.28569−1.20985 −0.15 −6.28953 3.2618 0.15 13.71771 −6.8869 0.7 −7.18194−1.5223 −0.15 −5.26466 3.56204 0.15 13.67969 −6.91554 0.7 −8.02425−1.83061 −0.15 −4.1754 3.79366 0.15 13.62346 −6.94157 0.7 −8.81221−2.12356 −0.15 −3.03106 3.93893 0.15 13.52571 −6.95086 0.7 −9.54504−2.39294 −0.15 −1.84449 3.98175 0.15 13.39486 −6.89906 0.7 −10.22075−2.63544 −0.15 −0.63182 3.90994 0.15 13.25165 −6.77682 0.7 −10.8368−2.85107 −0.15 0.58875 3.71751 0.15 13.08108 −6.60763 0.7 −11.39892−3.01584 −0.15 1.79898 3.4058 0.15 12.86892 −6.40214 0.7 −11.91216−3.08569 −0.15 2.98261 2.98281 0.15 12.61885 −6.15316 0.7 −12.36216−3.08656 −0.15 4.12661 2.46142 0.15 12.32948 −5.86011 0.7 −12.74121−3.0336 −0.15 5.22234 1.85869 0.15 12.00072 −5.52206 0.7 −13.04397−2.93931 −0.15 6.26572 1.19415 0.15 11.63268 −5.13907 0.7 −13.2686−2.82074 −0.15 7.25457 0.48516 0.15 11.22569 −4.71191 0.7 −13.42124−2.70019 −0.15 8.18807 −0.2527 0.15 10.78015 −4.24219 0.7 −13.51632−2.59799 −0.15 9.06703 −1.00461 0.15 10.29627 −3.73253 0.7 −13.57044−2.52553 −0.15 9.89318 −1.757 0.15 9.77374 −3.18691 0.7 −13.6041−2.47318 −0.15 10.66776 −2.49868 0.15 9.21153 −2.61066 0.7 −13.6041−2.47318 −0.1 11.39125 −3.22063 0.15 8.60862 −2.01006 0.7 −13.63818−2.41269 −0.1 12.06457 −3.91458 0.15 7.96396 −1.39225 0.7 −13.68058−2.32113 −0.1 12.68835 −4.5735 0.15 7.27601 −0.76588 0.7 −13.72688−2.17242 −0.1 13.2627 −5.19199 0.15 6.5433 −0.14084 0.7 −13.7481−1.95648 −0.1 13.78751 −5.76574 0.15 5.76502 0.47221 0.7 −13.70351−1.67658 −0.1 14.26273 −6.29137 0.15 4.94155 1.06235 0.7 −13.56504−1.35103 −0.1 14.68852 −6.76643 0.15 4.0749 1.61894 0.7 −13.32761−0.99612 −0.1 15.06519 −7.18935 0.15 3.16899 2.13227 0.7 −12.99678−0.6185 −0.1 15.39332 −7.55948 0.15 2.22947 2.59384 0.7 −12.57928−0.21894 −0.1 15.67389 −7.87713 0.15 1.26378 2.99724 0.7 −12.081750.20486 −0.1 15.90857 −8.14315 0.15 0.28094 3.33894 0.7 −11.507790.65301 −0.1 16.09997 −8.35909 0.15 −0.7093 3.61808 0.7 −10.853881.11557 −0.1 16.24743 −8.53063 0.15 −1.69704 3.83584 0.7 −10.1123 1.5726−0.1 16.32363 −8.68141 0.15 −2.67279 3.99473 0.7 −9.28131 2.00751 −0.116.32418 −8.79933 0.15 −3.62767 4.09804 0.7 −8.36291 2.40499 −0.116.29416 −8.86743 0.15 −4.55345 4.14962 0.7 −7.36204 2.7509 −0.116.25791 −8.91163 0.15 −5.44264 4.15397 0.7 −6.28647 3.03353 −0.116.21671 −8.94443 0.15 −6.28845 4.11487 0.7 −5.14618 3.24452 −0.116.15461 −8.97346 0.15 −7.08475 4.03649 0.7 −3.9525 3.37874 −0.1 16.0462−8.97992 0.15 −7.82621 3.92412 0.7 −2.71729 3.43353 −0.1 15.90354−8.91764 0.15 −8.50828 3.78304 0.7 −1.45254 3.40804 −0.1 15.74415−8.78348 0.15 −9.12719 3.61839 0.7 −0.17043 3.29918 −0.1 15.54932−8.60268 0.15 −9.68028 3.43644 0.7 1.11176 3.07649 −0.1 15.30795 −8.38240.15 −10.16686 3.24587 0.7 2.37469 2.73268 −0.1 15.02211 −8.11651 0.15−10.58953 3.05919 0.7 3.60234 2.27792 −0.1 14.6906 −7.80394 0.15−10.95377 2.89043 0.7 4.7826 1.72759 −0.1 14.31334 −7.44361 0.15−11.26498 2.74998 0.7 5.90763 1.10014 −0.1 13.89053 −7.03551 0.15−11.52504 2.6387 0.7 6.97341 0.41492 −0.1 13.42238 −6.58065 0.15−11.74148 2.57167 0.7 7.97885 −0.30924 −0.1 12.90904 −6.08115 0.15−11.91461 2.56034 0.7 8.92469 −1.05504 −0.1 12.35049 −5.5403 0.15−12.03443 2.59413 0.7 9.8124 −1.80733 −0.1 11.74646 −4.96262 0.15−12.09919 2.64226 0.7 10.64348 −2.55324 −0.1 11.09605 −4.35414 0.15−12.13231 2.68681 0.7 11.4193 −3.28188 −0.1 10.39763 −3.72278 0.15−11.98515 3.58516 0.8 12.14089 −3.98409 −0.1 9.64965 −3.07752 0.15−12.00356 3.63922 0.8 12.80897 −4.65225 −0.1 8.85019 −2.4292 0.15−12.00757 3.7221 0.8 13.42401 −5.28013 −0.1 7.99766 −1.79009 0.15−11.97106 3.84492 0.8 13.98622 −5.86283 −0.1 7.0914 −1.17361 0.15−11.87031 3.99221 0.8 14.49572 −6.3966 −0.1 6.13203 −0.59409 0.15−11.70107 4.15245 0.8 14.95258 −6.87888 −0.1 5.12197 −0.06662 0.15−11.46788 4.3265 0.8 15.35711 −7.30802 −0.1 4.06621 0.39422 0.15−11.17289 4.51713 0.8 15.70989 −7.68333 −0.1 2.97333 0.77731 0.15−10.81419 4.72171 0.8 16.01119 −8.00581 −0.1 1.85454 1.0754 0.15−10.38942 4.93498 0.8 16.26373 −8.27542 −0.1 0.72257 1.28484 0.15−9.89975 5.15677 0.8 16.46863 −8.4952 −0.1 −0.40907 1.40696 0.15−9.34523 5.38311 0.8 16.6285 −8.66821 −0.1 −1.52735 1.4473 0.15 −8.724985.60515 0.8 16.71595 −8.82081 −0.1 −2.62057 1.41428 0.15 −8.038545.81046 0.8 16.7234 −8.94341 −0.1 −3.67875 1.31786 0.15 −7.2874 5.986170.8 16.69494 −9.01548 −0.1 −4.69362 1.1685 0.15 −6.47538 6.12071 0.816.65855 −9.06259 −0.1 −5.65847 0.97668 0.15 −5.60833 6.20347 0.816.61765 −9.09686 −0.1 −6.56791 0.75216 0.15 −4.69389 6.2247 0.816.55536 −9.1276 −0.1 −7.41772 0.5043 0.15 −3.74131 6.17642 0.8 16.44562−9.13586 −0.1 −8.20493 0.2423 0.15 −2.76115 6.05231 0.8 16.29977 −9.0758−0.1 −8.92745 −0.02554 0.15 −1.76493 5.84804 0.8 16.13546 −8.94329 −0.1−9.58413 −0.29158 0.15 −0.76457 5.56195 0.8 15.93317 −8.76549 −0.1−10.17498 −0.54816 0.15 0.22834 5.19567 0.8 15.68303 −8.54856 −0.1−10.70131 −0.78734 0.15 1.20356 4.75446 0.8 15.38633 −8.28693 −0.1−11.16575 −1.0009 0.15 2.15303 4.24703 0.8 15.04134 −7.98015 −0.1−11.57089 −1.18283 0.15 3.07124 3.68456 0.8 14.64756 −7.62751 −0.1−11.91775 −1.33241 0.15 3.9545 3.07868 0.8 14.2047 −7.2295 −0.1−12.20973 −1.44503 0.15 4.80056 2.44091 0.8 13.7126 −6.78761 −0.1−12.44989 −1.5168 0.15 5.60878 1.783 0.8 13.17117 −6.30434 −0.1 −12.6403−1.54138 0.15 6.37911 1.11575 0.8 12.57932 −5.78441 −0.1 −12.77636−1.52011 0.15 7.1113 0.44838 0.8 11.9294 −5.24144 −0.1 −12.85398−1.47601 0.15 7.80489 −0.21108 0.8 11.21862 −4.68535 −0.1 −12.89472−1.43005 0.15 8.45947 −0.85542 0.8 10.44638 −4.12525 −0.1 −12.82023−1.1467 0.2 9.07451 −1.47838 0.8 9.61327 −3.57046 −0.1 −12.84951−1.08717 0.2 9.64894 −2.07491 0.8 8.72127 −3.03004 −0.1 −12.8642 −0.99190.2 10.18174 −2.64066 0.8 7.77385 −2.5124 −0.1 −12.84024 −0.84499 0.210.67209 −3.17185 0.8 6.77589 −2.02507 −0.1 −12.75518 −0.65595 0.211.11937 −3.66527 0.8 5.73338 −1.57462 −0.1 −12.60344 −0.4317 0.211.52326 −4.11829 0.8 4.6532 −1.16681 −0.1 −12.38659 −0.17241 0.211.88374 −4.52891 0.8 3.54286 −0.80691 −0.1 −12.09907 0.11707 0.212.20103 −4.89581 0.8 2.40968 −0.50224 −0.1 −11.74396 0.43957 0.212.4757 −5.21835 0.8 1.25768 −0.28039 −0.1 −11.31629 0.78881 0.212.70897 −5.49648 0.8 0.09743 −0.1604 −0.1 −10.8143 1.16022 0.2 12.90195−5.73116 0.8 −1.05581 −0.14881 −0.1 −10.23789 1.54988 0.2 13.06086−5.92043 0.8 −2.18639 −0.23453 −0.1 −9.58698 1.95236 0.2 13.17582−6.07628 0.8 −3.28192 −0.40174 −0.1 −8.86073 2.35893 0.2 13.21965−6.21428 0.8 −4.33362 −0.63216 −0.1 −8.05845 2.75818 0.2 13.20315−6.31392 0.8 −5.33587 −0.90754 −0.1 −7.18095 3.13796 0.2 13.17202−6.36955 0.8 −6.28569 −1.20985 −0.1 −6.23009 3.48377 0.2 13.13922−6.4059 0.8 −7.18194 −1.5223 −0.1 −5.20906 3.77793 0.2 13.10266 −6.433950.8 −8.02425 −1.83061 −0.1 −4.12412 4.00276 0.2 13.04869 −6.46017 0.8−8.81221 −2.12356 −0.1 −2.98465 4.13996 0.2 12.95441 −6.47237 0.8−9.54504 −2.39294 −0.1 −1.80377 4.17314 0.2 12.826 −6.42669 0.8−10.22075 −2.63544 −0.1 −0.59797 4.09001 0.2 12.68532 −6.31079 0.8−10.8368 −2.85107 −0.1 0.61419 3.88477 0.2 12.51917 −6.14798 0.8−11.39892 −3.01584 −0.1 1.81431 3.55949 0.2 12.31282 −5.94997 0.8−11.91216 −3.08569 −0.1 2.98645 3.12351 0.2 12.07048 −5.7091 0.8−12.36216 −3.08656 −0.1 4.11829 2.59096 0.2 11.78946 −5.42619 0.8−12.74121 −3.0336 −0.1 5.20156 1.97886 0.2 11.46939 −5.10058 0.8−13.04397 −2.93931 −0.1 6.23232 1.30625 0.2 11.1102 −4.7325 0.8 −13.2686−2.82074 −0.1 7.20886 0.59074 0.2 10.7122 −4.32268 0.8 −13.42124−2.70019 −0.1 8.13084 −0.15192 0.2 10.27597 −3.8725 0.8 −13.51632−2.59799 −0.1 8.99914 −0.90725 0.2 9.80192 −3.38435 0.8 −13.57044−2.52553 −0.1 9.81524 −1.66225 0.2 9.28977 −2.86207 0.8 −13.6041−2.47318 −0.1 10.58032 −2.40597 0.2 8.7385 −2.31094 0.8 −13.6041−2.47318 −0.05 11.29487 −3.12954 0.2 8.1474 −1.73687 0.8 −13.63818−2.41269 −0.05 11.95977 −3.82481 0.2 7.51585 −1.14645 0.8 −13.68058−2.32113 −0.05 12.5757 −4.48483 0.2 6.84291 −0.54755 0.8 −13.72688−2.17242 −0.05 13.14274 −5.10427 0.2 6.1278 0.05093 0.8 −13.7481−1.95648 −0.05 13.66077 −5.67887 0.2 5.37039 0.6396 0.8 −13.70351−1.67658 −0.05 14.12971 −6.20533 0.2 4.57165 1.20903 0.8 −13.56504−1.35103 −0.05 14.54973 −6.68121 0.2 3.73393 1.75013 0.8 −13.32761−0.99612 −0.05 14.92116 −7.10494 0.2 2.86106 2.25464 0.8 −12.99678−0.6185 −0.05 15.24463 −7.47584 0.2 1.95826 2.71532 0.8 −12.57928−0.21894 −0.05 15.52118 −7.79418 0.2 1.03215 3.1266 0.8 −12.081750.20486 −0.05 15.75243 −8.06082 0.2 0.09055 3.48502 0.8 −11.507790.65301 −0.05 15.94112 −8.27719 0.2 −0.85811 3.78895 0.8 −10.853881.11557 −0.05 16.08625 −8.44922 0.2 −1.80518 4.03833 0.8 −10.1123 1.5726−0.05 16.16046 −8.60004 0.2 −2.74215 4.23416 0.8 −9.28131 2.00751 −0.0516.15983 −8.71734 0.2 −3.66086 4.37832 0.8 −8.36291 2.40499 −0.0516.12937 −8.78483 0.2 −4.55359 4.47345 0.8 −7.36204 2.7509 −0.0516.09297 −8.82853 0.2 −5.41311 4.52321 0.8 −6.28647 3.03353 −0.0516.05163 −8.86096 0.2 −6.2329 4.53092 0.8 −5.14618 3.24452 −0.0515.98946 −8.88949 0.2 −7.00706 4.50073 0.8 −3.9525 3.37874 −0.0515.88124 −8.89519 0.2 −7.73046 4.43805 0.8 −2.71729 3.43353 −0.0515.73929 −8.83218 0.2 −8.39879 4.34775 0.8 −1.45254 3.40804 −0.0515.5811 −8.69733 0.2 −9.00833 4.23383 0.8 −0.17043 3.29918 −0.0515.38792 −8.51564 0.2 −9.5562 4.10092 0.8 1.11176 3.07649 −0.05 15.14874−8.29408 0.2 −10.04102 3.95613 0.8 2.37469 2.73268 −0.05 14.86566−8.0265 0.2 −10.46418 3.81089 0.8 3.60234 2.27792 −0.05 14.53763−7.71176 0.2 −10.82968 3.67866 0.8 4.7826 1.72759 −0.05 14.16468−7.34868 0.2 −11.14177 3.56959 0.8 5.90763 1.10014 −0.05 13.74709−6.93711 0.2 −11.40213 3.48458 0.8 6.97341 0.41492 −0.05 13.28518−6.47799 0.2 −11.6169 3.43973 0.8 7.97885 −0.30924 −0.05 12.77916−5.97336 0.2 −11.78477 3.44523 0.8 8.92469 −1.05504 −0.05 12.22901−5.42647 0.2 −11.89731 3.4885 0.8 9.8124 −1.80733 −0.05 11.63438 −4.84180.2 −11.95612 3.53992 0.8 10.64348 −2.55324 −0.05 10.99433 −4.22532 0.2−11.98515 3.58516 0.8 11.4193 −3.28188 −0.05 10.30724 −3.58476 0.2−11.82288 4.48627 0.9 12.14089 −3.98409 −0.05 9.57142 −2.929 0.2−11.83636 4.53963 0.9 12.80897 −4.65225 −0.05 8.78468 −2.2689 0.2−11.83441 4.61958 0.9 13.42401 −5.28013 −0.05 7.94504 −1.61687 0.2−11.79122 4.73525 0.9 13.98622 −5.86283 −0.05 7.05139 −0.98651 0.2−11.68433 4.86997 0.9 14.49572 −6.3966 −0.05 6.10398 −0.39239 0.2−11.50993 5.01152 0.9 14.95258 −6.87888 −0.05 5.10489 0.1502 0.2−11.27306 5.1616 0.9 15.35711 −7.30802 −0.05 4.05889 0.62655 0.2−10.97644 5.32463 0.9 15.70989 −7.68333 −0.05 2.97443 1.02536 0.2−10.61783 5.49717 0.9 16.01119 −8.00581 −0.05 1.86257 1.3389 0.2−10.19562 5.67479 0.9 16.26373 −8.27542 −0.05 0.73612 1.56331 0.2−9.71048 5.85646 0.9 16.46863 −8.4952 −0.05 −0.39126 1.70006 0.2−9.16249 6.03776 0.9 16.6285 −8.66821 −0.05 −1.5064 1.75483 0.2 −8.551166.20904 0.9 16.71595 −8.82081 −0.05 −2.59749 1.73592 0.2 −7.876676.35676 0.9 16.7234 −8.94341 −0.05 −3.65441 1.65294 0.2 −7.14149 6.467180.9 16.69494 −9.01548 −0.05 −4.66868 1.5159 0.2 −6.35071 6.52922 0.916.65855 −9.06259 −0.05 −5.63335 1.33484 0.2 −5.51136 6.53471 0.916.61765 −9.09686 −0.05 −6.54266 1.11877 0.2 −4.63171 6.47774 0.916.55536 −9.1276 −0.05 −7.39194 0.87623 0.2 −3.72082 6.35462 0.916.44562 −9.13586 −0.05 −8.1777 0.61582 0.2 −2.78811 6.16336 0.916.29977 −9.0758 −0.05 −8.8976 0.3459 0.2 −1.8432 5.90333 0.9 16.13546−8.94329 −0.05 −9.55039 0.07459 0.2 −0.89566 5.57538 0.9 15.93317−8.76549 −0.05 −10.13606 −0.19007 0.2 0.04539 5.18215 0.9 15.68303−8.54856 −0.05 −10.6559 −0.44006 0.2 0.97179 4.72846 0.9 15.38633−8.28693 −0.05 −11.11291 −0.66652 0.2 1.8769 4.22136 0.9 15.04134−7.98015 −0.05 −11.51084 −0.86145 0.2 2.75579 3.66965 0.9 14.64756−7.62751 −0.05 −11.85249 −1.02058 0.2 3.6048 3.0826 0.9 14.2047 −7.2295−0.05 −12.1396 −1.14331 0.2 4.42142 2.46966 0.9 13.7126 −6.78761 −0.05−12.37621 −1.22426 0.2 5.20427 1.84054 0.9 13.17117 −6.30434 −0.05−12.56531 −1.25489 0.2 5.95257 1.20442 0.9 12.57932 −5.78441 −0.05−12.70136 −1.23565 0.2 6.66549 0.56939 0.9 11.9294 −5.24144 −0.05−12.77905 −1.19207 0.2 7.34213 −0.05737 0.9 11.21862 −4.68535 −0.05−12.82023 −1.1467 0.2 7.98165 −0.66936 0.9 10.44638 −4.12525 −0.05−12.66507 −0.52212 0.3 8.58315 −1.26089 0.9 9.61327 −3.57046 −0.05−12.69517 −0.46403 0.3 9.14553 −1.82717 0.9 8.72127 −3.03004 −0.05−12.71238 −0.37052 0.3 9.66748 −2.36426 0.9 7.77385 −2.5124 −0.05−12.69142 −0.22522 0.3 10.14788 −2.86881 0.9 6.77589 −2.02507 −0.05−12.60742 −0.0388 0.3 10.58601 −3.3378 0.9 5.73338 −1.57462 −0.05−12.45419 0.17992 0.3 10.9817 −3.76853 0.9 4.6532 −1.16681 −0.05−12.23451 0.43069 0.3 11.33524 −4.15875 0.9 3.54286 −0.80691 −0.05−11.9495 0.71478 0.3 11.64692 −4.50714 0.9 2.40968 −0.50224 −0.05−11.59301 1.02586 0.3 11.91693 −4.81337 0.9 1.25768 −0.28039 −0.05−11.1639 1.36118 0.3 12.14598 −5.07777 0.9 0.09743 −0.1604 −0.05−10.66206 1.71823 0.3 12.33437 −5.30193 0.9 −1.05581 −0.14881 −0.05−10.08743 2.09336 0.3 12.48908 −5.48301 0.9 −2.18639 −0.23453 −0.05−9.43876 2.47933 0.3 12.59881 −5.6339 0.9 −3.28192 −0.40174 −0.05−8.71556 2.86776 0.3 12.63654 −5.7683 0.9 −4.33362 −0.63216 −0.05−7.91801 3.24874 0.3 12.61745 −5.86373 0.9 −5.33587 −0.90754 −0.05−7.04683 3.60986 0.3 12.58681 −5.91699 0.9 −6.28569 −1.20985 −0.05−6.10373 3.9361 0.3 12.55532 −5.95212 0.9 −7.18194 −1.5223 −0.05−5.09221 4.21023 0.3 12.52036 −5.97976 0.9 −8.02425 −1.83061 −0.05−4.01847 4.41357 0.3 12.46885 −6.00646 0.9 −8.81221 −2.12356 −0.05−2.89225 4.52765 0.3 12.37831 −6.02229 0.9 −9.54504 −2.39294 −0.05−1.7271 4.536 0.3 12.25215 −5.98407 0.9 −10.22075 −2.63544 −0.05−0.54002 4.42663 0.3 12.11322 −5.87569 0.9 −10.8368 −2.85107 −0.050.65017 4.19472 0.3 11.95065 −5.72026 0.9 −11.39892 −3.01584 −0.051.82531 3.84386 0.3 11.74937 −5.53065 0.9 −11.91216 −3.08569 −0.052.9703 3.38511 0.3 11.51385 −5.29897 0.9 −12.36216 −3.08656 −0.054.07412 2.83404 0.3 11.2409 −5.02665 0.9 −12.74121 −3.0336 −0.05 5.129472.20771 0.3 10.92938 −4.71385 0.9 −13.04397 −2.93931 −0.05 6.132941.52455 0.3 10.57855 −4.36142 0.9 −13.2686 −2.82074 −0.05 7.083580.80204 0.3 10.18854 −3.97027 0.9 −13.42124 −2.70019 −0.05 7.981560.05564 0.3 9.7602 −3.54144 0.9 −13.51632 −2.59799 −0.05 8.82766−0.70102 0.3 9.29445 −3.07673 0.9 −13.57044 −2.52553 −0.05 9.62305−1.45587 0.3 8.79117 −2.57979 0.9 −13.6041 −2.47318 −0.05 10.36888−2.19832 0.3 8.24915 −2.05606 0.9 −13.52552 −2.38409 0 11.06575 −2.91970.3 7.66812 −1.51093 0.9 −13.56009 −2.32419 0 11.71416 −3.61244 0.37.04795 −0.95041 0.9 −13.60476 −2.23415 0 12.31463 −4.26991 0.3 6.38834−0.38154 0.9 −13.65494 −2.08735 0 12.86726 −4.88688 0.3 5.68931 0.187940.9 −13.6775 −1.8724 0 13.37195 −5.45918 0.3 4.95148 0.74999 0.9−13.62635 −1.59473 0 13.82864 −5.98358 0.3 4.17639 1.29663 0.9 −13.47466−1.27667 0 14.23742 −6.45773 0.3 3.36668 1.82027 0.9 −13.22314 −0.933670 14.59864 −6.8801 0.3 2.52614 2.31398 0.9 −12.88125 −0.5687 0 14.91299−7.24996 0.3 1.65962 2.77174 0.9 −12.45657 −0.18011 0 15.18158 −7.56750.3 0.77296 3.18865 0.9 −11.95469 0.23455 0 15.40603 −7.83361 0.3−0.12716 3.56118 0.9 −11.379 0.67583 0 15.58936 −8.04942 0.3 −1.033563.88703 0.9 −10.72496 1.13277 0 15.72976 −8.22135 0.3 −1.93878 4.164980.9 −9.98464 1.58537 0 15.79976 −8.37164 0.3 −2.83535 4.39471 0.9−9.15673 2.01828 0 15.79658 −8.48731 0.3 −3.71589 4.57682 0.9 −8.242942.41659 0 15.76546 −8.55338 0.3 −4.57321 4.71291 0.9 −7.24767 2.76603 015.72901 −8.59602 0.3 −5.40045 4.80605 0.9 −6.17809 3.05433 0 15.68765−8.6277 0.3 −6.19135 4.85933 0.9 −5.04365 3.27199 0 15.62573 −8.655360.3 −6.94024 4.87736 0.9 −3.85532 3.4117 0 15.51837 −8.6603 0.3 −7.642234.86619 0.9 −2.62504 3.46894 0 15.37805 −8.59687 0.3 −8.29333 4.830410.9 −1.36527 3.44135 0 15.22241 −8.46174 0.3 −8.89013 4.77284 0.9−0.08886 3.32495 0 15.03291 −8.27943 0.3 −9.42988 4.69666 0.9 1.186563.09309 0 14.79831 −8.05699 0.3 −9.91099 4.60789 0.9 2.44197 2.74121 014.52102 −7.78811 0.3 −10.3339 4.51693 0.9 3.66169 2.27981 0 14.20009−7.47156 0.3 −10.70069 4.43501 0.9 4.83394 1.72438 0 13.83574 −7.106 0.3−11.01337 4.36862 0.9 5.95125 1.09344 0 13.42841 −6.69116 0.3 −11.273394.3184 0.9 7.00985 0.4062 0 12.97857 −6.22783 0.3 −11.48493 4.30241 0.98.00869 −0.31887 0 12.48649 −5.71793 0.3 −11.64505 4.3294 0.9 8.94848−1.06474 0 11.9522 −5.16457 0.3 −11.74775 4.38459 0.9 9.83067 −1.81653 011.37535 −4.5721 0.3 −11.79895 4.44013 0.9 10.65679 −2.56145 0 10.75487−3.94643 0.3 −11.82288 4.48627 0.9 11.42811 −3.28883 0 10.08899 −3.295090.3 −11.61042 5.36982 1 12.14561 −3.98962 0 9.37607 −2.62659 0.3−11.61833 5.4222 1 12.80996 −4.65628 0 8.61357 −1.9516 0.3 −11.609055.49863 1 13.4216 −5.2827 0 7.79893 −1.2826 0.3 −11.55685 5.60539 113.98072 −5.86401 0 6.93038 −0.63335 0.3 −11.44283 5.72539 1 14.48744−6.39645 0 6.0076 −0.01846 0.3 −11.26425 5.84726 1 14.94178 −6.87755 05.03226 0.5469 0.3 −11.02392 5.97011 1 15.344 −7.3057 0 4.00874 1.048190.3 −10.72598 6.10193 1 15.69452 −7.68038 0 2.94492 1.47362 0.3−10.36844 6.23936 1 15.99433 −8.00191 0 1.85141 1.81477 0.3 −9.950026.37833 1 16.24535 −8.27096 0 0.74091 2.06766 0.3 −9.47078 6.51607 116.44911 −8.49021 0 −0.37286 2.23374 0.3 −8.93096 6.64745 1 16.60796−8.66291 0 −1.47669 2.31848 0.3 −8.33072 6.7621 1 16.69436 −8.81532 0−2.55871 2.32971 0.3 −7.67127 6.84482 1 16.7013 −8.93747 0 −3.608592.27623 0.3 −6.95664 6.8814 1 16.67266 −9.00914 0 −4.61759 2.16717 0.3−6.19337 6.86271 1 16.63632 −9.05599 0 −5.57832 2.01156 0.3 −5.389356.78327 1 16.59546 −9.09011 0 −6.48445 1.81708 0.3 −4.55294 6.64073 116.53333 −9.12077 0 −7.33054 1.59092 0.3 −3.69204 6.43671 1 16.42385−9.12901 0 −8.1123 1.34072 0.3 −2.81406 6.17395 1 16.27838 −9.06912 0−8.82667 1.07452 0.3 −1.92611 5.8555 1 16.11451 −8.93692 0 −9.471960.80072 0.3 −1.03513 5.48452 1 15.91315 −8.75909 0 −10.04806 0.52823 0.3−0.14781 5.06452 1 15.66393 −8.54239 0 −10.55656 0.26634 0.3 0.729574.59973 1 15.36837 −8.281 0 −11.00118 0.02532 0.3 1.5915 4.09543 115.02478 −7.9744 0 −11.38709 −0.18474 0.3 2.43329 3.55779 1 14.63268−7.62191 0 −11.71788 −0.35865 0.3 3.25092 2.99334 1 14.19202 −7.22371 0−11.99536 −0.49599 0.3 4.04122 2.4091 1 13.7023 −6.78168 0 −12.22498−0.5896 0.3 4.80197 1.81264 1 13.16363 −6.2981 0 −12.4113 −0.62662 0.35.53146 1.21137 1 12.5751 −5.77743 0 −12.54645 −0.60938 0.3 6.228130.61207 1 11.92986 −5.23224 0 −12.62376 −0.56668 0.3 6.89049 0.02095 111.2252 −4.67209 0 −12.66507 −0.52212 0.3 7.51727 −0.55616 1 10.46065−4.10561 0 −12.51061 0.1717 0.4 8.10732 −1.11404 1 9.63674 −3.54173 0−12.54055 0.22853 0.4 8.65952 −1.64807 1 8.75508 −2.98957 0 −12.558630.32011 0.4 9.1724 −2.15465 1 7.81854 −2.45804 0 −12.5389 0.46289 0.49.64458 −2.6308 1 6.83124 −1.95566 0 −12.4546 0.64507 0.4 10.07524−3.0737 1 5.79851 −1.49018 0 −12.29962 0.85654 0.4 10.4643 −3.48062 14.72677 −1.06865 0 −12.07818 1.09758 0.4 10.81225 −3.84914 1 3.62328−0.69744 0 −11.79155 1.36949 0.4 11.11978 −4.1776 1 2.49558 −0.38403 0−11.43451 1.66663 0.4 11.38695 −4.46578 1 1.34851 −0.15263 0 −11.005251.98538 0.4 11.61337 −4.715 1 0.19262 −0.01998 0 −10.50476 2.32471 0.411.79868 −4.92735 1 −0.95741 0.00772 0 −9.9323 2.67998 0.4 11.94954−5.09997 1 −2.08636 −0.05959 0 −9.28695 3.04427 0.4 12.05445 −5.24566 1−3.18184 −0.20728 0 −8.5684 3.4093 0.4 12.08552 −5.37643 1 −4.23478−0.41847 0 −7.77685 3.76492 0.4 12.06397 −5.4676 1 −5.23911 −0.67573 0−6.91327 4.09881 0.4 12.03375 −5.51843 1 −6.19121 −0.96212 0 −5.97984.3964 0.4 12.00365 −5.55245 1 −7.08916 −1.26211 0 −4.98029 4.64063 0.411.97051 −5.58 1 −7.93208 −1.56202 0 −3.9213 4.81293 0.4 11.92181−5.60787 1 −8.71935 −1.85065 0 −2.81301 4.89543 0.4 11.83556 −5.62937 1−9.45022 −2.11964 0 −1.66929 4.87252 0.4 11.71064 −5.6039 1 −10.12304−2.36479 0 −0.50721 4.73326 0.4 11.57173 −5.50523 1 −10.73618 −2.58365 00.65472 4.47408 0.4 11.41598 −5.3534 1 −11.29463 −2.75549 0 1.799144.09983 0.4 11.22267 −5.16861 1 −11.8024 −2.85084 0 2.91213 3.62258 0.410.99252 −4.94701 1 −12.2499 −2.88584 0 3.9841 3.05864 0.4 10.72459−4.6877 1 −12.63131 −2.86939 0 5.0087 2.4247 0.4 10.41849 −4.39008 1−12.94169 −2.80856 0 5.98287 1.73809 0.4 10.07415 −4.05438 1 −13.17669−2.71385 0 6.90623 1.01582 0.4 9.69155 −3.6816 1 −13.3376 −2.60549 07.77936 0.27293 0.4 9.2707 −3.2736 1 −13.43657 −2.50754 0 8.60289−0.47789 0.4 8.8116 −2.83306 1 −13.49174 −2.43616 0 9.37754 −1.22551 0.48.3143 −2.36345 1 −13.52552 −2.38409 0 10.10438 −1.95983 0.4 7.77884−1.86891 1 −13.3513 −2.17712 0.033 10.78404 −2.6724 0.4 7.2053 −1.354421 −13.38705 −2.11864 0.033 11.41667 −3.35622 0.4 6.59387 −0.82556 1−13.43504 −2.03134 0.033 12.00244 −4.00513 0.4 5.945 −0.28842 1−13.48756 −1.88683 0.033 12.54134 −4.61412 0.4 5.25952 0.2505 1−13.50129 −1.67307 0.033 13.03324 −5.17914 0.4 4.53883 0.78453 1−13.42291 −1.40442 0.033 13.4781 −5.69702 0.4 3.78499 1.30708 1 −13.2409−1.10639 0.033 13.87606 −6.16542 0.4 3.00097 1.81198 1 −12.96716 −0.78580.033 14.22753 −6.58278 0.4 2.19059 2.29363 1 −12.61117 −0.44092 0.03314.53322 −6.94838 0.4 1.35836 2.74706 1 −12.17814 −0.06947 0.03314.79424 −7.26239 0.4 0.50939 3.16785 1 −11.67152 0.33011 0.033 15.01209−7.52574 0.4 −0.35069 3.55228 1 −11.09399 0.75824 0.033 15.19023−7.73917 0.4 −1.21587 3.89742 1 −10.43985 1.20255 0.033 15.32579−7.90981 0.4 −2.07986 4.20095 1 −9.70237 1.64498 0.033 15.39125 −8.058860.4 −2.93621 4.46133 1 −8.88093 2.07232 0.033 15.3855 −8.1723 0.4−3.77833 4.67808 1 −7.97682 2.47066 0.033 15.354 −8.23671 0.4 −4.599594.85204 1 −6.99348 2.82568 0.033 15.31779 −8.27822 0.4 −5.39346 4.985831 −5.9368 3.12371 0.033 15.27677 −8.30917 0.4 −6.15389 5.08286 1−4.81508 3.35279 0.033 15.21558 −8.33619 0.4 −6.87534 5.14855 1 −3.638623.50204 0.033 15.1097 −8.34116 0.4 −7.55306 5.18969 1 −2.41949 3.562990.033 14.97119 −8.27879 0.4 −8.1833 5.21139 1 −1.17104 3.52989 0.03314.81822 −8.14489 0.4 −8.76311 5.21625 1 0.09229 3.39678 0.033 14.63269−7.96363 0.4 −9.29017 5.20611 1 1.35228 3.1455 0.033 14.40297 −7.742470.4 −9.76279 5.18434 1 2.59065 2.77641 0.033 14.13179 −7.4749 0.4−10.1803 5.15799 1 3.79233 2.30048 0.033 13.81818 −7.15971 0.4 −10.543085.13599 1 4.94625 1.73359 0.033 13.46246 −6.79553 0.4 −10.85193 5.122741 6.04587 1.0947 0.033 13.06514 −6.38204 0.4 −11.10801 5.11957 1 7.087870.40261 0.033 12.62674 −5.91994 0.4 −11.31184 5.14275 1 8.07125 −0.324980.033 12.14764 −5.41103 0.4 −11.45973 5.19564 1 8.9967 −1.07172 0.03311.62791 −4.8583 0.4 −11.54978 5.2635 1 9.86569 −1.82308 0.033 11.06719−4.26599 0.4 −11.59218 5.32298 1 10.67976 −2.56657 0.033 10.46438−3.63987 0.4 −11.61042 5.36982 1 11.44002 −3.29191 0.033 9.81775 −2.98720.4 −11.35102 6.33666 1.1 12.14737 −3.99032 0.033 9.12564 −2.3162 0.4−11.35253 6.38774 1.1 12.80244 −4.65442 0.033 8.38546 −1.63721 0.4−11.33618 6.46018 1.1 13.40556 −5.27827 0.033 7.59444 −0.96241 0.4−11.27654 6.55808 1.1 13.95686 −5.85713 0.033 6.75054 −0.30526 0.4−11.15574 6.66251 1.1 14.45647 −6.38732 0.033 5.85308 0.31991 0.4−10.97213 6.76142 1.1 14.90438 −6.86639 0.033 4.90344 0.89841 0.4−10.72931 6.85539 1.1 15.3008 −7.29283 0.033 3.9057 1.41625 0.4−10.43054 6.95288 1.1 15.64622 −7.66602 0.033 2.86709 1.86171 0.4−10.07429 7.05095 1.1 15.94167 −7.98626 0.033 1.79759 2.22604 0.4−9.65987 7.14652 1.1 16.18897 −8.25431 0.033 0.70944 2.50515 0.4−9.18752 7.23733 1.1 16.38994 −8.4725 0.033 −0.38402 2.70019 0.4−8.65738 7.31591 1.1 16.5462 −8.64475 0.033 −1.46982 2.8161 0.4 −8.070327.36935 1.1 16.63013 −8.79677 0.033 −2.53622 2.85986 0.4 −7.429357.38227 1.1 16.63576 −8.9179 0.033 −3.57291 2.83928 0.4 −6.74029 7.341331.1 16.60685 −8.98873 0.033 −4.57098 2.76243 0.4 −6.01103 7.2383 1.116.57057 −9.03497 0.033 −5.52277 2.63737 0.4 −5.24999 7.07031 1.116.52973 −9.06874 0.033 −6.42153 2.47057 0.4 −4.4648 6.83935 1.116.46772 −9.09899 0.033 −7.26131 2.26811 0.4 −3.6615 6.55108 1.116.35872 −9.10709 0.033 −8.0372 2.03686 0.4 −2.84474 6.21279 1.116.21392 −9.04729 0.033 −8.74551 1.78439 0.4 −2.01854 5.83143 1.116.05121 −8.91506 0.033 −9.38398 1.51906 0.4 −1.18703 5.4127 1.115.85165 −8.73693 0.033 −9.95216 1.25018 0.4 −0.35471 4.961 1.1 15.60441−8.52009 0.033 −10.45159 0.98779 0.4 0.47362 4.48017 1.1 15.31141−8.25834 0.033 −10.88639 0.74326 0.4 1.29326 3.97407 1.1 14.97089−7.95124 0.033 −11.26249 0.52792 0.4 2.09946 3.44643 1.1 14.58246−7.59803 0.033 −11.58422 0.34802 0.4 2.88739 2.90079 1.1 14.14655−7.19837 0.033 −11.8539 0.20472 0.4 3.65314 2.34184 1.1 13.66215−6.75466 0.033 −12.0778 0.10629 0.4 4.39349 1.77488 1.1 13.12967−6.26881 0.033 −12.26102 0.06709 0.4 5.10564 1.20529 1.1 12.54855−5.74485 0.033 −12.39426 0.08464 0.4 5.78719 0.63842 1.1 11.91402−5.19269 0.033 −12.47003 0.1276 0.4 6.43614 0.07965 1.1 11.22375−4.62087 0.033 −12.51061 0.1717 0.4 7.05092 −0.46581 1.1 10.47714−4.03749 0.033 −12.36836 0.93896 0.5 7.63 −0.9933 1.1 9.67425 −3.451240.033 −12.39699 0.99483 0.5 8.17194 −1.4987 1.1 8.81566 −2.8717 0.033−12.41389 1.08449 0.5 8.67551 −1.97825 1.1 7.90291 −2.30895 0.033−12.3928 1.22379 0.5 9.13974 −2.42872 1.1 6.93861 −1.77333 0.033−12.30653 1.40001 0.5 9.56383 −2.84736 1.1 5.92673 −1.27492 0.033−12.14906 1.60217 0.5 9.94726 −3.23195 1.1 4.87249 −0.82364 0.033−11.92514 1.83067 0.5 10.28985 −3.58075 1.1 3.78257 −0.42858 0.033−11.63683 2.08757 0.5 10.59184 −3.89251 1.1 2.66499 −0.09796 0.033−11.27887 2.36686 0.5 10.8538 −4.16652 1.1 1.52667 0.15099 0.033−10.84958 2.66487 0.5 11.07736 −4.40214 1.1 0.3786 0.30635 0.033−10.35067 2.98174 0.5 11.26276 −4.60099 1.1 −0.76544 0.36363 0.033−9.78149 3.31292 0.5 11.41525 −4.76115 1.1 −1.89111 0.33072 0.033−9.14063 3.65047 0.5 11.51015 −4.90608 1.1 −2.9862 0.21974 0.033−8.42767 3.98553 0.5 11.53355 −5.03354 1.1 −4.04117 0.045 0.033 −7.643194.30797 0.5 11.51018 −5.12084 1.1 −5.04904 −0.1785 0.033 −6.788644.60584 0.5 11.48064 −5.16963 1.1 −6.00499 −0.43597 0.033 −5.866684.8648 0.5 11.4517 −5.20253 1.1 −6.90597 −0.7134 0.033 −4.88184 5.068470.5 11.41983 −5.22958 1.1 −7.75008 −0.99822 0.033 −3.84139 5.19957 0.511.37314 −5.25754 1.1 −8.53612 −1.27981 0.033 −2.75594 5.24179 0.511.29012 −5.28096 1.1 −9.26318 −1.54958 0.033 −1.63946 5.18129 0.511.16793 −5.26228 1.1 −9.93025 −1.80148 0.033 −0.50857 5.00887 0.511.02775 −5.17461 1.1 −10.5372 −2.02919 0.033 0.6192 4.72233 0.510.87506 −5.02896 1.1 −11.08828 −2.21582 0.033 1.7278 4.32734 0.510.68769 −4.84954 1.1 −11.58442 −2.35184 0.033 2.80473 3.83617 0.510.46337 −4.63567 1.1 −12.0223 −2.44144 0.033 3.84176 3.26502 0.510.20178 −4.38584 1.1 −12.39981 −2.48615 0.033 4.8334 2.62979 0.59.90219 −4.09987 1.1 −12.71475 −2.48738 0.033 5.77696 1.94663 0.59.56425 −3.77825 1.1 −12.9638 −2.44717 0.033 6.67238 1.2317 0.5 9.18782−3.4221 1.1 −13.14317 −2.37544 0.033 7.52036 0.49925 0.5 8.77289−3.03329 1.1 −13.25559 −2.29428 0.033 8.32133 −0.23894 0.5 8.31955−2.61439 1.1 −13.31623 −2.22802 0.033 9.07563 −0.97262 0.5 7.82798−2.16868 1.1 −13.3513 −2.17712 0.033 9.78412 −1.69227 0.5 7.29846−1.70008 1.1 −13.17386 −1.95084 0.067 10.4473 −2.38983 0.5 6.73145−1.21306 1.1 −13.20828 −1.89231 0.067 11.06491 −3.05888 0.5 6.1277−0.71253 1.1 −13.25195 −1.8038 0.067 11.63684 −3.69368 0.5 5.48832−0.20366 1.1 −13.29584 −1.65793 0.067 12.16294 −4.28948 0.5 4.814920.30825 1.1 −13.28697 −1.4459 0.067 12.64303 −4.84235 0.5 4.109660.81797 1.1 −13.17947 −1.19039 0.067 13.07702 −5.34924 0.5 3.37531.32044 1.1 −12.97711 −0.90976 0.067 13.46503 −5.80788 0.5 2.615151.8109 1.1 −12.69137 −0.60517 0.067 13.80748 −6.21673 0.5 1.833 2.284841.1 −12.32858 −0.27425 0.067 14.10505 −6.57509 0.5 1.03303 2.73798 1.1−11.89204 0.08478 0.067 14.35889 −6.88307 0.5 0.2197 3.16626 1.1−11.38424 0.47305 0.067 14.5704 −7.14165 0.5 −0.6023 3.56573 1.1−10.8071 0.89039 0.067 14.74369 −7.35094 0.5 −1.42807 3.93267 1.1−10.15336 1.32207 0.067 14.87426 −7.51922 0.5 −2.25247 4.26368 1.1−9.41884 1.7538 0.067 14.9349 −7.66634 0.5 −3.07005 4.55611 1.1 −8.603252.17371 0.067 14.92667 −7.77706 0.5 −3.87499 4.80847 1.1 −7.707622.56849 0.067 14.89501 −7.83959 0.5 −4.66116 5.02095 1.1 −6.734752.92383 0.067 14.85934 −7.87991 0.5 −5.42225 5.19613 1.1 −5.689643.22521 0.067 14.81902 −7.91016 0.5 −6.15218 5.33848 1.1 −4.579783.45898 0.067 14.75903 −7.93675 0.5 −6.84534 5.45437 1.1 −3.4149 3.611760.067 14.65523 −7.94259 0.5 −7.49686 5.55114 1.1 −2.20709 3.67183 0.06714.51879 −7.88268 0.5 −8.10292 5.63436 1.1 −0.97053 3.63023 0.06714.36856 −7.75156 0.5 −8.66076 5.7066 1.1 0.27889 3.47924 0.067 14.18733−7.57299 0.5 −9.16843 5.76822 1.1 1.52254 3.20822 0.067 13.96278−7.35524 0.5 −9.62454 5.81944 1.1 2.74299 2.82171 0.067 13.69797−7.09156 0.5 −10.02795 5.86371 1.1 3.92577 2.33118 0.067 13.39188−6.78087 0.5 −10.37785 5.90708 1.1 5.06058 1.75283 0.067 13.04478−6.42186 0.5 −10.67431 5.95232 1.1 6.14173 1.10591 0.067 12.65713−6.01427 0.5 −10.91815 5.99992 1.1 7.1663 0.40876 0.067 12.22946−5.55877 0.5 −11.10671 6.06356 1.1 8.13337 −0.32164 0.067 11.76221−5.05704 0.5 −11.23625 6.1438 1.1 9.04361 −1.06954 0.067 11.25552−4.51194 0.5 −11.30912 6.22537 1.1 9.89855 −1.82074 0.067 10.70906−3.9276 0.5 −11.33996 6.28917 1.1 10.6997 −2.56313 0.067 10.12172−3.30963 0.5 −11.35102 6.33666 1.1 11.44803 −3.28678 0.067 9.49189−2.66504 0.5 −11.22132 6.84537 1.15 12.14437 −3.98314 0.067 8.81806−2.00166 0.5 −11.21964 6.89562 1.15 12.78928 −4.64505 0.067 8.09775−1.32942 0.5 −11.20014 6.96604 1.15 13.38305 −5.26669 0.067 7.32832−0.65997 0.5 −11.13706 7.05955 1.15 13.92576 −5.84344 0.067 6.50775−0.00618 0.5 −11.01279 7.15568 1.15 14.41745 −6.37176 0.067 5.63540.61834 0.5 −10.82696 7.24274 1.15 14.85823 −6.84913 0.067 4.712571.19981 0.5 −10.58343 7.32226 1.15 15.24838 −7.27398 0.067 3.74311.72516 0.5 −10.28467 7.40205 1.15 15.5883 −7.6458 0.067 2.73365 2.183260.5 −9.92961 7.48024 1.15 15.87904 −7.96485 0.067 1.69339 2.56557 0.5−9.5176 7.55351 1.15 16.12236 −8.23195 0.067 0.63377 2.86802 0.5−9.04902 7.62004 1.15 16.32034 −8.44914 0.067 −0.43262 3.09127 0.5−8.52421 7.67155 1.15 16.47376 −8.62103 0.067 −1.49345 3.2394 0.5−7.94463 7.69403 1.15 16.55498 −8.77271 0.067 −2.53741 3.3183 0.5−7.31418 7.6723 1.15 16.5592 −8.89276 0.067 −3.55438 3.3345 0.5 −6.639587.59349 1.15 16.52995 −8.96267 0.067 −4.53549 3.29487 0.5 −5.929297.44981 1.15 16.4937 −9.00824 0.067 −5.47298 3.20641 0.5 −5.191877.23943 1.15 16.45282 −9.04168 0.067 −6.35989 3.07454 0.5 −4.434446.96584 1.15 16.39092 −9.07157 0.067 −7.18999 2.90444 0.5 −3.662076.63625 1.15 16.28226 −9.07927 0.067 −7.958 2.70232 0.5 −2.87786 6.259861.15 16.13824 −9.01903 0.067 −8.65974 2.47513 0.5 −2.08403 5.84574 1.1515.97674 −8.8865 0.067 −9.29234 2.23062 0.5 −1.28329 5.4008 1.1515.77894 −8.70781 0.067 −9.85472 1.97779 0.5 −0.47905 4.93026 1.1515.53383 −8.49029 0.067 −10.34796 1.72688 0.5 0.32467 4.43815 1.1515.24331 −8.22784 0.067 −10.77617 1.49007 0.5 1.12328 3.92765 1.1514.90595 −7.91965 0.067 −11.14565 1.27984 0.5 1.91189 3.40145 1.1514.5214 −7.56491 0.067 −11.46125 1.10338 0.5 2.68558 2.86228 1.1514.08963 −7.16382 0.067 −11.72553 0.96235 0.5 3.43975 2.31328 1.1513.6106 −6.71768 0.067 −11.94546 0.86655 0.5 4.17039 1.75827 1.1513.08437 −6.22876 0.067 −12.12575 0.83075 0.5 4.8742 1.2017 1.1512.51064 −5.70076 0.067 −12.25599 0.85113 0.5 5.5485 0.64841 1.1511.88657 −5.1412 0.067 −12.3293 0.89502 0.5 6.19107 0.10332 1.1511.21045 −4.5575 0.067 −12.36836 0.93896 0.5 6.80002 −0.42879 1.1510.48118 −3.95778 0.067 −12.26099 1.80558 0.6 7.37373 −0.94348 1.159.69802 −3.35107 0.067 −12.28694 1.86081 0.6 7.91084 −1.43657 1.158.86066 −2.74744 0.067 −12.30077 1.94841 0.6 8.41011 −1.90442 1.157.9695 −2.15786 0.067 −12.27584 2.08307 0.6 8.87042 −2.34399 1.157.02602 −1.59385 0.067 −12.18524 2.25087 0.6 9.2909 −2.75265 1.156.03301 −1.06721 0.067 −12.02442 2.44108 0.6 9.67104 −3.12819 1.154.99467 −0.58997 0.067 −11.79838 2.65464 0.6 10.01078 −3.46877 1.153.91718 −0.17328 0.067 −11.50782 2.89226 0.6 10.3105 −3.773 1.15 2.808890.17388 0.067 −11.14935 3.14966 0.6 10.57103 −4.03993 1.15 1.678450.43914 0.067 −10.72133 3.42321 0.6 10.79284 −4.27001 1.15 0.53730.61411 0.067 −10.22498 3.71244 0.6 10.97768 −4.46339 1.15 −0.601230.69601 0.067 −9.66009 4.01346 0.6 11.1286 −4.62014 1.15 −1.723420.69137 0.067 −9.02551 4.31842 0.6 11.22279 −4.76223 1.15 −2.81730.61055 0.067 −8.32049 4.61717 0.6 11.24085 −4.8884 1.15 −3.873040.46591 0.067 −7.54562 4.89868 0.6 11.21482 −4.97344 1.15 −4.883070.2706 0.067 −6.70295 5.151 0.6 11.18504 −5.02101 1.15 −5.84174 0.03770.067 −5.79601 5.36049 0.6 11.15656 −5.05338 1.15 −6.7451 −0.2201 0.067−4.83035 5.51238 0.6 11.12539 −5.08042 1.15 −7.59042 −0.4913 0.067−3.81413 5.59188 0.6 11.07992 −5.10904 1.15 −8.37584 −0.76589 0.067−2.7583 5.5854 0.6 10.99899 −5.13544 1.15 −9.10014 −1.03529 0.067−1.67642 5.48194 0.6 10.87778 −5.12179 1.15 −9.76266 −1.29211 0.067−0.58394 5.2748 0.6 10.73884 −5.03617 1.15 −10.3639 −1.52837 0.0670.50328 4.96309 0.6 10.5879 −4.89267 1.15 −10.90804 −1.72854 0.0671.57085 4.55217 0.6 10.40337 −4.71515 1.15 −11.39421 −1.89116 0.0672.60745 4.05302 0.6 10.18176 −4.50426 1.15 −11.82198 −2.01521 0.0673.60597 3.481 0.6 9.92352 −4.25773 1.15 −12.19123 −2.09978 0.067 4.561782.85115 0.6 9.62694 −3.9764 1.15 −12.50193 −2.14415 0.067 5.47226 2.1780.6 9.29204 −3.66037 1.15 −12.7533 −2.14845 0.067 6.33748 1.47671 0.68.91864 −3.31083 1.15 −12.94297 −2.11569 0.067 7.15838 0.76091 0.68.50655 −2.9298 1.15 −13.0685 −2.05798 0.067 7.93535 0.04169 0.6 8.05585−2.51988 1.15 −13.13664 −1.99992 0.067 8.66838 −0.67162 0.6 7.5668−2.08427 1.15 −13.17387 −1.95085 0.067 9.35787 −1.3703 0.6 7.03982−1.62669 1.15 −13.01732 −1.72285 0.1 10.00415 −2.04674 0.6 6.47562−1.15135 1.15 −13.04412 −1.66127 0.1 10.60668 −2.69501 0.6 5.87525−0.66275 1.15 −13.05473 −1.56425 0.1 11.16491 −3.30995 0.6 5.24016−0.16558 1.15 −13.03338 −1.4151 0.1 11.67844 −3.88716 0.6 4.572330.33548 1.15 −12.96801 −1.21564 0.1 12.1469 −4.42298 0.6 3.87426 0.835841.15 −12.84428 −0.97102 0.1 12.57004 −4.91457 0.6 3.14898 1.33112 1.15−12.64173 −0.69517 0.1 12.94784 −5.35981 0.6 2.39998 1.81719 1.15−12.35886 −0.39415 0.1 13.28073 −5.7572 0.6 1.6311 2.29007 1.15−11.99986 −0.06708 0.1 13.56955 −6.10586 0.6 0.84642 2.74586 1.15−11.56697 0.28661 0.1 13.81561 −6.40578 0.6 0.05009 3.18059 1.15−11.06165 0.66653 0.1 14.02032 −6.65783 0.6 −0.75366 3.59009 1.15−10.4849 1.07094 0.1 14.18846 −6.86151 0.6 −1.56051 3.97017 1.15−9.83204 1.48818 0.1 14.31378 −7.02628 0.6 −2.36593 4.31678 1.15−9.10136 1.9079 0.1 14.3691 −7.17074 0.6 −3.16498 4.62664 1.15 −8.292382.31861 0.1 14.35809 −7.2781 0.6 −3.95216 4.89793 1.15 −7.40576 2.70720.1 14.32644 −7.33842 0.6 −4.72148 5.13084 1.15 −6.44376 3.05914 0.114.29152 −7.37739 0.6 −5.46669 5.328 1.15 −5.41063 3.35898 0.1 14.25225−7.40677 0.6 −6.18159 5.49445 1.15 −4.31313 3.59102 0.1 14.194 −7.432920.6 −6.86039 5.6372 1.15 −3.16072 3.73965 0.1 14.09306 −7.44007 0.6−7.49802 5.76397 1.15 −1.96578 3.7907 0.1 13.95954 −7.38354 0.6 −8.090545.88022 1.15 −0.74346 3.73306 0.1 13.81308 −7.25625 0.6 −8.63523 5.987691.15 0.48903 3.55925 0.1 13.63739 −7.08183 0.6 −9.13042 6.08547 1.151.71328 3.26604 0.1 13.41918 −6.86963 0.6 −9.57502 6.17241 1.15 2.912652.86035 0.1 13.16183 −6.61274 0.6 −9.96783 6.2508 1.15 4.07345 2.354060.1 12.86413 −6.31027 0.6 −10.30769 6.32566 1.15 5.18634 1.76385 0.112.52625 −5.96106 0.6 −10.59463 6.3983 1.15 6.24651 1.10905 0.1 12.14853−5.56492 0.6 −10.82904 6.47029 1.15 7.2514 0.40731 0.1 11.73147 −5.122530.6 −11.00731 6.55277 1.15 8.20011 −0.3252 0.1 11.27544 −4.63558 0.6−11.12629 6.64478 1.15 9.0933 −1.0734 0.1 10.7806 −4.10684 0.6 −11.189516.73229 1.15 9.93261 −1.82339 0.1 10.24654 −3.54041 0.6 −11.213996.79781 1.15 10.71942 −2.56357 0.1 9.67219 −2.94177 0.6 −11.221326.84537 1.15

In the above table, the plane Z′=0 corresponds to the reference plane P0situated at the base of the profile. This plane P0 is the intersectionof the stacking axis AE of the set of blades with the axisymmetricsurface of the hub, i.e. it passes via the intersection between the axisAE and the surface 12A where it is assembled with the platform 12. Theplane Z′=1 corresponds to the reference plane P1 situated at the top ofthe profile. This plane P1 is the intersection between the axis AE andthe axisymmetric surface of the casing, i.e. it passes via theintersection of the axis AE with the surface 16A where it is assembledwith the top platform 16.

By convention, the stacking axis AE of the set of blades, for the bladeof a rotary wheel, is the axis that extends in the radial direction Zand passes through the barycenter of the profile of the blade in sectionin the X, Y planes. This is the axis on which the various X,Y sectionsof the set of blades are “stacked” when designing the set of blades.

As mentioned at the beginning of the present description, theaerodynamic profile of the invention is substantially identical to thenominal profile defined in the above table, i.e. it departs from saidnominal profile by very little at most, being defined in particularwithin an envelope of ±1 mm in a direction normal to the surface of thenominal profile, and/or having X,Y coordinates lying within a range of±5% relative to the coordinates X,Y of the nominal profile.

The coordinates of the above table are given starting from a value Z′=0in the reference plane P0. The coordinate Z′ is non-dimensional, i.e.for a point P, situated at a distance D from the plane P0 (where D ismeasured along the axis Z), the value of Z′ is D/H, where H representsthe total height of the profile as measured between the planes P0 andP1. Naturally, in the table above, by multiplying the coordinate Z′ bythe height H, it is possible to obtain the complete coordinates of theblade.

In the above table, the profile is characterized by fifteen sections atconstant Z′ coordinates, for which the coordinates X and Y arespecified. In each section plane at constant coordinate Z′, the sectionof the profile is given by a continuous and smooth curve,interconnecting all of the points (X,Y). In each section plane, theprofile is interpolated so as to generate a uniform profile.

Preferably, the height H of the profile of the blade lies in the range140 centimeters (cm) to 200 cm, e.g. being about 167 cm. The referenceplane P0 is at a distance lying in the range 280 cm to 370 cm,preferably about 331 cm, from the axis A of the turbine.

FIG. 3 is a diagram of a section of the profile 14 in a plane X,Yparallel to the plane P0. As stated above, the blade R4 is in particulara blade of the rotary wheel of the fourth stage of a turbine. This bladeis therefore rotary, and it rotates in the direction of arrow R.

It is advantageous for the rotary wheel that includes the blade of theinvention to have 120 to 140 blades that present aerodynamic profiles asdefined above.

1. An aerodynamic profile for a turbine blade, the profile being, whencold and in a non-coated state, substantially identical to a nominalprofile determined by the Cartesian coordinates X,Y,Z′ given in Table 1,in which the coordinate Z′ is the quotient D/H, where D is the distanceof the point under consideration from a first reference X,Y planesituated at the base of the nominal profile, and H is the height of saidprofile measured from said first reference plane that is theintersection of the stacking axis of the set of blades and theaxisymmetric surface of the hub, out to a second reference plane that isthe intersection of said stacking axis with the axisymmetric surface ofthe casing, the measurements D and H being taken radially relative tothe axis of the turbine, while the coordinate X is measured in the axialdirection of the turbine.
 2. The aerodynamic profile as claimed in claim1, wherein said profile is defined within an envelope of ±1 mm in adirection normal to the surface of the nominal profile.
 3. Theaerodynamic profile as claimed in claim 1, wherein the coordinates X,Yof said profile lie within a range of ±5% relative to the coordinatesX,Y of the nominal profile.
 4. The aerodynamic profile as claimed inclaim 1, wherein the blade is a blade of a rotary wheel forming aportion of a rotor of a turbine.
 5. The aerodynamic profile as claimedin claim 4, wherein the blade is a blade of the rotary wheel of thefourth stage of the turbine.
 6. The aerodynamic profile as claimed inclaim 4, wherein the blade is a blade of the rotary wheel of the fourthstage of a turbine having four stages.
 7. A turbine blade, presenting anaerodynamic profile as claimed in claim
 1. 8. A turbine, includingturbine blades presenting aerodynamic profiles as claimed in claim
 1. 9.A turbine as claimed in claim 8, including a rotary wheel, having 120 to140 blades.
 10. A rotary wheel of a turbine forming a portion of aturbine rotor, wherein all the blades of this rotary wheel present anaerodynamic profile as claimed in claim
 1. 11. The rotary wheel of aturbine as claimed in claim 10, including 120 to 140 blades.